Universal Fluctuations in Spectra of Disordered Systems at the Anderson Transition

概要

論文の詳細を見る
Using the level-spacing distribution and the total probability function of the numbers of levels in a given energy interval we analyze the crossover of the level statistics between the delocalized and the localized regimes. By numerically calculating the electron spectra of systems of up to 32^3 lattice sites described by the Anderson Hamiltonian it is shown that the distribution P(s) of neighboring spacings is scale-independent at the metal-insulator transition. For large spacings it has a Poisson-like asymptotic form P(s)∝exp (-As/△), where A≈1.9. At the critical point we obtain a linear relationship between the variance of the number of levels <[δn(ε)]^2> and their average number <n(ε)> within the interval ε. The constant of proportionality is less than unity due to the repulsion of the levels. Both P (s) and <[δn(ε)]^2> are determined by the probability density Q_n(ε) of having exactly n levels in the energy interval ε. The distribution Q_n(ε) at the critical point is found to be size-independent and to obey a Gaussian law near its maximum, where n〜<n>.
社団法人応用物理学会の論文
1995-08-30